splitter is represented by a Hadamard operation(22), which transforms the initial photon state|0〉s into the superposition ðj0〉s þ j1〉s Þ=ffiffiffi2p.AHere, on the contrary, the presence of the sec-ond beamsplitter depends on the state of an an-cillary photon. If the ancilla photon is preparedin the state |0〉a, no beamsplitter is present; hence,the interferometer is left open. Formally, this cor-responds to the identity operator acting on |y〉s,resulting in the statetook. The measured intensities are ID′ = cos2(ϕ/2)and ID″ = sin2(ϕ/2).

To achieve our main goal—to refute models
in which the photon knows in advance with
which setup it will be confronted—we must go
one step further. Indeed, the result of Fig. 3 does
not refute such models. Although we have inserted the ancilla photon in a superposition, hence
testing both wave and particle aspects at the same
time, we have in fact not checked the quantum
nature of this superposition. This is because the
final measurement of the ancilla photon was made
in the logical ({|0〉a, |1〉a}) basis. Therefore, we cannot exclude the fact that the ancilla may have been
in a statistical mixture of the form cos2a|0〉〈0|a +
sin2a|1〉〈1|a, which would lead to the same measured statistics. Hence, the data can be explained
by a classical model, in which the state of the
ancilla represents a classical variable (a classical
bit) indicating which measurement, particle or
wave, will be performed. Because the state of the
ancilla may have been known to the system photon in advance—indeed, here no delayed choice
is performed by the observer—no conclusion can
be drawn from this experiment. This loophole
also plagues the recent theoretical proposal of
(17), as well as two of its NMR implementations
(19, 20).

In order to show that the measurement choice
could not have been known in advance, we must
ensure that our quantum controlled beamsplitter
behaves in a genuine quantum way. In particular,
we must ensure that it creates entanglement between the system and ancilla photons, which is the
clear signature of a quantum process. The global
state of the system and ancilla photons, given in
Eq. 3, is entangled for all values 0 < a < p/2.
Because 〈yparticle|ywave〉 ∼ cosϕ, the degree of
entanglement depends on ϕ and a; in particular,
for a = p/4 and ϕ = p/2 the state in Eq. 3 is
maximally entangled.

In order to certify the presence of this entan-glement, we tested the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality (25), the violation|Yf (a,ϕ)〉 = cosa|y〉s,particle|0〉a +sina| y〉s,wave|1〉a (3)

We fabricated the quantum circuit shown in
Fig. 2 in a silica-on-silicon photonic chip (18).
The Hadamard operation is implemented by a
directional coupler of reflectivity 1/2, which is
equivalent to a 50/50 beamsplitter. The controlled-Hadamard (CH) is based on a nondeterministic
control-phase gate (23, 24). The system and ancilla photon pairs are generated at 808 nm via
parametric down conversion and detected with
silicon avalanche photodiodes at the circuit’s
output.

We first characterized the behavior of oursetup for various quantum states of the an-cilla photon. We measured the output intensitiesID′(ϕ, a) and ID″(ϕ, a) for a ∈ [0, p/2], and ϕ ∈[−p/2, 3 p/2]. In particular, by increasing thevalue of a we observe the morphing betweena particle measurement (a = 0) and a wave mea-surement (a = p/2). For a = 0 (no beamsplitter),the measured intensities are independent of ϕ.For a = p/2, the beamsplitter is present, and theThe final measurement (in the {|0〉s, |1〉s} basis)indicates which path the photon took, revealingthe particle nature of the photon. The measuredintensities in both output modes are equal andphase-independent, ID′ = ID″ = 1/2.

Fig. 2. Implementationof the quantum delayed-choice experiment on areconfigurable integratedphotonic device. Non-entangled photon pairsare generated by usingtype I parametric down-conversion and injectedinto the chip by usingpolarization maintainingfibers (not shown). Thesystem photon (s), in thelower part of the circuit,enters the interferometer at the Hadamard gate (H). A relative phase ϕ isapplied between the two modes of the interferometer. Then, the controlled-Hadamard (CH) is implemented by a nondeterministic CZ gate with twoadditional MZ interferometers. The ancilla photon (a), in the top part of thecircuit, is controlled by the phase shifter a, which determines the quantumstate of the second beamsplitter—a superposition of present and absent.Last, the local measurements for the Bell test are performed through single-qubit rotations (UA and UB) followed by APDs. The circuit is composed ofdirectional couplers of reflectivity 1/2 (dc1−5 and dc9−13) and 1/3 (dc6−8) andresistive heaters (orange rectangles) that implement the phase shifters (25).